With the advent and wide spread use of computers a number of algorithms have been developed to determine the optimum ultimate pit limits in open pit mining. The main objective of these algorithms is to find groups of blocks that should be removed to yield the maximum overall mining profit under specified economic conditions and technological constraints. The most common methods are: Lerchs and Grossmann algorithm based on graph theory, the Korobov algorithm, floating or moving cone method, moving cone II and dynamic programming. Among these, the Lerchs-Grossmann algorithm is the only method that always yields the true optimum pit. The disadvantages of the algorithm are complexity of the method and require more computing time than other methods to find out optimum pit outline. The floating cone approach which does not yield a true optimum pit in some cases is the most popular and simplest method and requires significantly less computing time than any other method to reach a solution. The moving cone II has been developed by Wright to overcome the shortfalls of the floating cone method. In this paper the moving cone II has been evaluated for being as a true optimum open pit design method and also two algorithms has been proposed for modification of this method. For this purpose C++ computer programs have been developed under Windows operating system for these algorithms and their results are compared with the Lerchs and Grossmann method, which is the true optimum open pit design algorithm. The outcomes show that these algorithms are able to produce good results.